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Chapter 1．INTRODUCTORY 1

1．Biological assay 1

2．Variability of response 3

3．Statistical methods 5

4．Summary of constants 6

Chapter 2．QUANTAL RESPONSES AND THE DOSAGE-RESPONSE CURVE 8

5．The frequency distribution of tolerance 8

6．Direct measurement of tolerance 12

7．The binomial distribution 14

8．The median effective dose 17

8．1．Notation and terminology 19

Chapter 3．THE ESTIMATION OF THE MEDIAN EFFECTIVE DOSE 20

9．The probit transformation 20

10．The probit regression line 22

11．Precision of the estimates 31

12．Fiducial probability 36

13．Approximate methods of estimation 37

14．History of the probit method 42

15．Alternative tolerance distributions 46

Chapter 4．THE MAXIMUM LIKELIHOOD SOLUTION 48

16．Working probits 48

17．The regression equation 51

18．Heterogeneity 55

19．Fiducial limits 61

Chapter 5．THE COMPARISON OF EFFECTIVENESS 65

20．Relative potency 65

21．Combination and comparison of relative potencies 73

22．Design of experiments 81

23．Precision of assays 83

24．Mean probit difference 85

25．Unequal tolerance variances 86

Chapter 6．ADJUSTMENTS FOR NATURAL MORTALITY 88

26．Abbott＇s formula 88

27．Approximate estimation of the parameters 89

28．The maximum likelihood estimates 91

Chapter 7．FACTORIAL EXPERIMENTS 100

29．Reasons for factorial design 100

30．Qualitative factors 103

31．The probit plane 103

32．Ostwald＇s equation 114

33．The interaction of two factors 116

34．Extensions to several factors 120

Chapter 8．THE TOXIC ACTION OF MIXTURES OF POISONS 122

35．Types of joint action 122

36．Similar action 124

37．A general test for similar action 130

38．Independent action 136

39．Synergistic action 146

40．Planned tests of synergism and similarity 150

41．Compound response curves 153

Chapter 9．MISCELLANEOUS PROBLEMS 160

42．Variation between batches 160

43．Individual mortality records 165

44．The average kill 170

45．The Parker-Rhodes equation 172

Chapter 10．GRADED RESPONSES 183

46．The linear dosage-response curve 183

47．Quantitative responses and the probit transformation 185

48．Semiquantal responses 197

Chapter 11．RECENT DEVELOPMENTS 199

49．Alternatives to maximum likelihood estimation 199

50．Wadley＇s problem 203

51．A factorial experiment 205

52．Incomplete replication in complex experiments 211

53．Theory of independent action 215

54．Estimation of a percentage point 218

55．Staircase estimation 226

56．The meaning of standard errors 232

Appendix Ⅰ．THE COMPUTING OF PROBIT ANALYSES 236

Appendix Ⅱ．MATHEMATICAL BASIS OF THE PROBIT METHOD 246

References 255

Tables 264

Ⅰ．Transformation of percentages to probits 264

Ⅱ．The weighting coefficient and Q/Z 268

Ⅲ．Maximum and minimum working probits and range 295

Ⅳ．Working probits 296

Ⅴ．The probability,P．the ordinate,Z,and Z2 306

Ⅵ．Distribution of X2 307

Ⅶ．Distribution of i 308

Ⅷ．The weighting coefficient in Wadley＇s problem 309

Ⅸ．Minimum working probit,range,and weighting coefficient for inverse sampling 310

Index of Authors 311

Index of Subjects 313